Paul is looking at Linda; Linda is looking at John. Paul is married; John is not married. Is someone who is married looking at someone who is not married? A. Yes B. No C. Can't tell
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one. On Fri, May 5, 2017 at 03:15 Henry Baker <hbaker1@pipeline.com> wrote:
Paul is looking at Linda; Linda is looking at John.
Paul is married; John is not married.
Is someone who is married looking at someone who is not married?
A. Yes B. No C. Can't tell
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Nice, thank you Victor! à+ É. Catapulté de mon aPhone
Le 5 mai 2017 à 10:36, Victor Miller <victorsmiller@gmail.com> a écrit :
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
On Fri, May 5, 2017 at 03:15 Henry Baker <hbaker1@pipeline.com> wrote:
Paul is looking at Linda; Linda is looking at John.
Paul is married; John is not married.
Is someone who is married looking at someone who is not married?
A. Yes B. No C. Can't tell
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On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no. I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic. -- g
Does this mean that when most people read the question, they think of marriage as being a binary predicate (i.e. relation): m : X x X --> {true, false} rather than as a unary predicate (i.e. property): m : X --> {true, false} and thus fail to resolve the question? It would be interesting to see what happens if you replace 'married' with 'wearing red trousers' (something which is intuitively a unary predicate rather than a binary predicate). I thought that the 'trick' was that there might be two Lindae in the question, in which case the following comic is pertinent: https://xkcd.com/169/ Best wishes, Adam P. Goucher
Sent: Friday, May 05, 2017 at 10:59 AM From: "Gareth McCaughan" <gareth.mccaughan@pobox.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Brain teaser
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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Indeed. Or 'Winklevoses', since it derives etymologically not from the Greek 'Winklevos', but is instead a back-formation from the English word 'Winklevology': https://mathoverflow.net/a/60915/39521 -- APG.
Sent: Friday, May 05, 2017 at 6:25 PM From: "Gareth McCaughan" <gareth.mccaughan@pobox.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Brain teaser
On 05/05/2017 12:20, Veit Elser wrote:
One of my favorite moments in “The Social Network” was when the Zuckerberg character refers to the Harvard twins as “the Winklevii”.
It ought to be "Winklevoi", though.
-- g
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I thought you were going to reference https://xkcd.com/246/ Charles Greathouse Case Western Reserve University On Fri, May 5, 2017 at 6:49 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Does this mean that when most people read the question, they think of marriage as being a binary predicate (i.e. relation):
m : X x X --> {true, false}
rather than as a unary predicate (i.e. property):
m : X --> {true, false}
and thus fail to resolve the question?
It would be interesting to see what happens if you replace 'married' with 'wearing red trousers' (something which is intuitively a unary predicate rather than a binary predicate).
I thought that the 'trick' was that there might be two Lindae in the question, in which case the following comic is pertinent:
Best wishes,
Adam P. Goucher
Sent: Friday, May 05, 2017 at 10:59 AM From: "Gareth McCaughan" <gareth.mccaughan@pobox.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Brain teaser
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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Huh? The explanation is much more likely to be that the question is subtly ambiguous. The unsociable interpret "is looking at" literally as an asymmetrical relation, so tick C; the sociable (apparently!) assume that the phrase implies both parties are "looking at" one another, so tick A. As to option B, I am unable to arrive at any conclusion which does not reflect unflatteringly on the neurological apparatus of the responder ... WFL On 5/5/17, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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Even in the unsociable interpretation, A is still the correct box to tick. In particular, there is a directed path: Paul --> Linda --> John such that Paul is married and John is unmarried. Hence, there must be a pair of adjacent nodes X --> Y such that X is married and Y is not married. -- APG.
Sent: Friday, May 05, 2017 at 12:05 PM From: "Fred Lunnon" <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Brain teaser
Huh? The explanation is much more likely to be that the question is subtly ambiguous. The unsociable interpret "is looking at" literally as an asymmetrical relation, so tick C; the sociable (apparently!) assume that the phrase implies both parties are "looking at" one another, so tick A.
As to option B, I am unable to arrive at any conclusion which does not reflect unflatteringly on the neurological apparatus of the responder ...
WFL
On 5/5/17, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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Ah, but then there are the folks who are SO trained in mathematics that they immediately see the proof that there is a married person who is looking at a non-married person but they feel that the proof is unsatisfyingly nonconstructive; while they are trying to come up with a nonclassical logic in which it might be possible for there to be no such person, the interrogator insists on an immediate answer, so the mathematician says "I think the answer is 'I don't know,' but I'm not sure." Jim On Friday, May 5, 2017, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the
married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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<< This particular question has been posed to large numbers of people (college students, mostly, because they are readily available and free), and only 10-20% get it right. >> So what IS "the" answer, and why exactly is it "right" ? [ Interesting to speculate how a battery of such innocent-looking questions at a job interview could result in a --- possibly unintentional and undetectable --- bias favouring candidates neurologically similar to the examiners! ] WFL On 5/5/17, James Propp <jamespropp@gmail.com> wrote:
Ah, but then there are the folks who are SO trained in mathematics that they immediately see the proof that there is a married person who is looking at a non-married person but they feel that the proof is unsatisfyingly nonconstructive; while they are trying to come up with a nonclassical logic in which it might be possible for there to be no such person, the interrogator insists on an immediate answer, so the mathematician says "I think the answer is 'I don't know,' but I'm not sure."
Jim
On Friday, May 5, 2017, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the
married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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This discussion reminds me of a central defect of multiple-choice tests. If the person taking the test comes up with a "wrong" answer, then it means (very roughly speaking) that the test-taker is either smarter than OR stupider than the test-designer, but from the answer alone it is impossible to determine which. (Actually, I like Fred Lunnon's way of looking at things: in many cases it's not about "smart" or "stupid", but rather about neurological similarity.) Jim On Fri, May 5, 2017 at 8:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
<< This particular question has been posed to large numbers of people (college students, mostly, because they are readily available and free), and only 10-20% get it right. >>
So what IS "the" answer, and why exactly is it "right" ?
[ Interesting to speculate how a battery of such innocent-looking questions at a job interview could result in a --- possibly unintentional and undetectable --- bias favouring candidates neurologically similar to the examiners! ]
WFL
On 5/5/17, James Propp <jamespropp@gmail.com> wrote:
Ah, but then there are the folks who are SO trained in mathematics that they immediately see the proof that there is a married person who is looking at a non-married person but they feel that the proof is unsatisfyingly nonconstructive; while they are trying to come up with a nonclassical logic in which it might be possible for there to be no such person, the interrogator insists on an immediate answer, so the mathematician says "I think the answer is 'I don't know,' but I'm not sure."
Jim
On Friday, May 5, 2017, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the
married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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this problem generated a lot of traffic last year in the guardian https://www.google.com/amp/s/amp.theguardian.com/science/2016/mar/28/did-you... On Fri, May 5, 2017 at 7:07 AM James Propp <jamespropp@gmail.com> wrote:
This discussion reminds me of a central defect of multiple-choice tests. If the person taking the test comes up with a "wrong" answer, then it means (very roughly speaking) that the test-taker is either smarter than OR stupider than the test-designer, but from the answer alone it is impossible to determine which.
(Actually, I like Fred Lunnon's way of looking at things: in many cases it's not about "smart" or "stupid", but rather about neurological similarity.)
Jim
On Fri, May 5, 2017 at 8:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
<< This particular question has been posed to large numbers of people (college students, mostly, because they are readily available and free), and only 10-20% get it right. >>
So what IS "the" answer, and why exactly is it "right" ?
[ Interesting to speculate how a battery of such innocent-looking questions at a job interview could result in a --- possibly unintentional and undetectable --- bias favouring candidates neurologically similar to the examiners! ]
WFL
On 5/5/17, James Propp <jamespropp@gmail.com> wrote:
Ah, but then there are the folks who are SO trained in mathematics that they immediately see the proof that there is a married person who is looking at a non-married person but they feel that the proof is unsatisfyingly nonconstructive; while they are trying to come up with a nonclassical logic in which it might be possible for there to be no such person, the interrogator insists on an immediate answer, so the mathematician says "I think the answer is 'I don't know,' but I'm not sure."
Jim
On Friday, May 5, 2017, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the
married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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What if Linda is in a coherent superposition of being married and unmarried at the same time? This ties in with what we might call the "Schrodinger's Wife" paradox. According to http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-quantum-mechanics... , *Schrodinger lavishly thanked his physicist friend Hermann Weyl for his help with the mathematics. (He was perhaps indebted to Weyl for an even greater favor: Weyl regularly bedded down Schrodinger's wife, Anny, so that Schrodinger was free to seek elsewhere the erotic inspiration he needed for his work.)* I suggest that Schrodinger's wife Anny was in just such a quantum superposition. In any case, I propose that we replace "Paul", "Linda", and "John" in this discussion by "Erwin", "Anny", and "Hermann", and end this baseless (if subtle) calumny of the Beatles. (See http://thediaryjunction.blogspot.com/2009/03/lennon-and-linda-mccartney.html for a definitive repudiation of the Linda-and-John legend.) Jim Propp On Fri, May 5, 2017 at 7:39 AM, James Propp <jamespropp@gmail.com> wrote:
Ah, but then there are the folks who are SO trained in mathematics that they immediately see the proof that there is a married person who is looking at a non-married person but they feel that the proof is unsatisfyingly nonconstructive; while they are trying to come up with a nonclassical logic in which it might be possible for there to be no such person, the interrogator insists on an immediate answer, so the mathematician says "I think the answer is 'I don't know,' but I'm not sure."
Jim
On Friday, May 5, 2017, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the
married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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Of course, the worlds of 20th century physics and 20th century pop music are also joined together by the enigma of whether Paul (like Schrodonger's cat) is, or isn't, dead. Jim On Friday, May 5, 2017, James Propp <jamespropp@gmail.com> wrote:
What if Linda is in a coherent superposition of being married and unmarried at the same time?
This ties in with what we might call the "Schrodinger's Wife" paradox. According to http://www.nytimes.com/1990/01/07/books/the-lone-ranger- of-quantum-mechanics.html?pagewanted=all,
*Schrodinger lavishly thanked his physicist friend Hermann Weyl for his help with the mathematics. (He was perhaps indebted to Weyl for an even greater favor: Weyl regularly bedded down Schrodinger's wife, Anny, so that Schrodinger was free to seek elsewhere the erotic inspiration he needed for his work.)*
I suggest that Schrodinger's wife Anny was in just such a quantum superposition.
In any case, I propose that we replace "Paul", "Linda", and "John" in this discussion by "Erwin", "Anny", and "Hermann", and end this baseless (if subtle) calumny of the Beatles. (See http://thediaryjunction. blogspot.com/2009/03/lennon-and-linda-mccartney.html for a definitive repudiation of the Linda-and-John legend.)
Jim Propp
On Fri, May 5, 2017 at 7:39 AM, James Propp <jamespropp@gmail.com <javascript:_e(%7B%7D,'cvml','jamespropp@gmail.com');>> wrote:
Ah, but then there are the folks who are SO trained in mathematics that they immediately see the proof that there is a married person who is looking at a non-married person but they feel that the proof is unsatisfyingly nonconstructive; while they are trying to come up with a nonclassical logic in which it might be possible for there to be no such person, the interrogator insists on an immediate answer, so the mathematician says "I think the answer is 'I don't know,' but I'm not sure."
Jim
On Friday, May 5, 2017, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the
married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
-- g
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I suspect it would make a difference in how many people got the answer if the persons were named Paul, Bob, and John. Brent On 5/5/2017 2:59 AM, Gareth McCaughan wrote:
On 05/05/2017 09:36, Victor Miller wrote:
Is there some trick? If Linda is married, then the Linda-John pair is the married/not married pair. If Linda isn't married then the Paul/lLinda pair is the one.
The only trick is that a surprising number of people, even rather clever people, get only as far as figuring out that they can't tell whether L&J are married nor whether P&L are married, and conclude that the answer to the question is no.
I think it likely that training in mathematics correlates strongly with answering this correctly. I am not sure how the explanation for this, if I'm right, should be divided between the effect of learning about logic and the effect of being the sort of person who is willing to spend time learning about logic.
participants (11)
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Brent Meeker -
Charles Greathouse -
Eric Angelini -
Fred Lunnon -
Gareth McCaughan -
Henry Baker -
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Veit Elser -
Victor Miller